To reduce the detection complexity of the space-time bit-interleaved coded modulation(ST-BICM) scheme, a turbo type iterative receiver structure consisting of a new group Gaussian approximation(GGA) algorithm and an a posteriori probability(APP) decoder is presented. When calculating the log-likelihood ratio(LLR) of the i-th transmitted symbol, the GGA algorithm first divide the N transmitted signals into two groups, a detecting group consisting of G signals with the i-th transmitted signal included, and an interfering group consisting of the other N-G signals. Taking the superposition of the N-G signals as a Gaussian random variable, the GGA algorithm implements the maximum a posteriori(MAP) detection to obtain the LLR of the signal transmitted from antenna i. At high SNR values or if the receiver has more than two replicas of each transmitted signal, the GGA detection exhibits a good performance as well as low decoding complexity.